Question: Vanessa is 28 years older than Stephanie. Twenty years ago, Vanessa was 5 times as old as Stephanie. How old is Stephanie now?
Answer: We can use the given information to write down two equations that describe the ages of Vanessa and Stephanie. Let Vanessa's current age be $v$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $v = s + 28$ Twenty years ago, Vanessa was $v - 20$ years old, and Stephanie was $s - 20$ years old. The information in the second sentence can be expressed in the following equation: $v - 20 = 5(s - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to use our first equation for $v$ and substitute it into our second equation. Our first equation is: $v = s + 28$ . Substituting this into our second equation, we get the equation: $(s + 28)$ $-$ $20 = 5(s - 20)$ which combines the information about $s$ from both of our original equations. Simplifying both sides of this equation, we get: $s + 8 = 5 s - 100$ Solving for $s$ , we get: $4 s = 108$ $s = 27$.